Suggestion to rig & animate skin+bone+muscle at the same time?
If the skin mesh is low or mid-poly:


Rig the skin with bones (automatic or manual weight painting).
Control the muscles inside the skin with Mesh Deform modifier set to skin object.
Parent the bone meshes to rig bones, they do not need to deform.


If the skin mesh is highpoly (ie. scanned or sculpted mesh):


Build a low poly envelope around your arm.
Control both the skin and muscles through Mesh Deform driven by the low poly.
Parent the bone meshes to rig bones.


The Mesh Deform modifier will ensure that the muscles will stay inside the skin and will deform correctly. You can add shapekeys to the muscles and skin to make them flex and preserve volume.

It is difficult to weight paint multiple meshes to the same bones to have the same deformation. The automatic heat-driven weigh painting will fail on separate meshes - this works well only on volumetric auto-weight painting that Maya has.